In this paper, we deal with sequential testing of multiple hypotheses. In the general scheme of construction of optimal tests based on the backward induction, we propose a modification which provides a simplified (generally speaking, suboptimal) version of the optimal test, for any particular criterion of optimization. We call this DBC version (the one with Dropped Backward Control) of the optimal test. In particular, for the case of two simple hypotheses, dropping backward control in the Bayesian test produces the classical sequential probability ratio test (SPRT). Similarly, dropping backward control in the modified Kiefer-Weiss solutions produces Lorden's 2-SPRTs . In the case of more than two hypotheses, we obtain in this way new classes of sequential multi-hypothesis tests, and investigate their properties. The efficiency of the DBC-tests is evaluated with respect to the optimal Bayesian multi-hypothesis test and with respect to the matrix sequential probability ratio test (MSPRT) by Armitage. In a multihypothesis variant of the Kiefer-Weiss problem for binomial proportions the performance of the DBC-test is numerically compared with that of the exact solution. In a model of normal observations with a linear trend, the performance of of the DBC-test is numerically compared with that of the MSPRT. Some other numerical examples are presented. In all the cases the proposed tests exhibit a very high efficiency with respect to the optimal tests (more than 99.3\% when sampling from Bernoulli populations) and/or with respect to the MSPRT (even outperforming the latter in some scenarios).

翻译：本文研究多重假设的序贯检验问题。在基于后向归纳法构建最优检验的一般框架下，我们提出了一种改进方法，该方法可为任意特定优化准则提供最优检验的简化版本（通常为次优解）。我们将这种最优检验的变体称为DBC版本（即舍弃后向控制的版本）。特别地，对于两个简单假设的情况，在贝叶斯检验中舍弃后向控制可导出经典的序贯概率比检验（SPRT）。类似地，在修正的Kiefer-Weiss解中舍弃后向控制可导出Lorden的2-SPRT。对于多于两个假设的情形，通过该方法我们获得了一系列新的序贯多重假设检验类别，并研究了它们的性质。DBC检验的效率评估分别以最优贝叶斯多重假设检验和Armitage的矩阵序贯概率比检验（MSPRT）为基准。在针对二项比例的Kiefer-Weiss问题多重假设变体中，通过数值计算比较了DBC检验与精确解的性能。在线性趋势正态观测模型中，通过数值计算比较了DBC检验与MSPRT的性能。文中还提供了其他数值算例。在所有案例中，所提检验相对于最优检验（在伯努利总体中抽样时效率超过99.3%）和/或相对于MSPRT（在某些场景中甚至优于后者）均表现出极高的效率。